My impression is that a lot of scholars share your skepticism. It's hard enough to solidly identify compositional history in documents that we actually have.
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NoahMar 11 '13 at 1:17

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Great question! Theories on the origin, composition, and redaction of Q is so diverse that it seems one can scarcely find two scholars who agree with each other. It's hard enough to find scholars agreeing with each other on exactly what Q contained: they that Q is a series of sayings of Jesus, and most would agree that certain sayings are a part of it, but beyond that there is little agreement. There are even some that disagree on the language Q was written in. I'm genuinely curious to see how they claim to manage to work their way back through the redaction of a document they don't have.
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NiobiusOct 22 '13 at 15:09

1 Answer
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The existence of Q was first inferred by 19th century German theologians from a statement made by the 2nd century bishop Papias of Hierapolis. Papias is quoted in Eusebius' History of the Church as saying, "Matthew wrote the oracles in the Hebrew language, and every one interpreted them as he was able." (History of the Church, 3.39.16). The Germans pointed out that this could not refer to our present Gospel of Matthew, which is not merely a collection of oracles and was not written in Hebrew. German philosopher Christian Hermann Weisse postulated that such a collection of oracles or sayings was a source of the common material found in Matthew and Luke.

By comparing the material found in both Matthew and Luke but not Mark, scholars have attempted to reconstruct this alleged source--and what they found was that it was not merely a collection of sayings, and it was probably written in Greek.

At its core, Q does contain a set of Jesus' sayings, for example, his teaching on love for enemies (found in Matthew 5:38-48 || Luke 6:27-36).

But it also contains expanded versions of stories also found in Mark, for example, the preaching of John the Baptist. (See Mark 1:1-8 || Matthew 3:1-12 || Luke 3:1-17). Here and elsewhere there is a pattern: The material unique to Q involves talk of judgment. Kloppenborg identified the judgment theme as a second stage of composition, added on top of the basic sayings of Jesus.

Finally, Q contains the narrative about Jesus' temptation in the desert. (Matthew 4:1-11 || Luke 4:1-13). This again is an expanded version of a passage that also appears in Mark. But unlike the rest of the Q content, this is a narrative. Kloppenborg considers this a third layer, composed later than the teachings found through the rest of the document.